Control system with response time estimation

ABSTRACT

A control system for a plant includes a controller configured to detect a disturbance in the control system. In response to detecting the disturbance, the controller is configured to evaluate a signal affected by the disturbance to estimate a response time of a plant. The response time is a parameter that characterizes a response of the plant to the disturbance. The controller is configured to adjust an operating parameter used by the control system based on the estimated response time. The controller is configured to use the adjusted operating parameter to generate and provide an input to the plant.

CROSS-REFERENCE TO RELATED PATENT APPLICATION

This application is a continuation of U.S. patent application Ser. No.13/794,683 filed Mar. 11, 2013, now U.S. Pat. No. 9,395,708, the entiredisclosure of which is incorporated by reference herein.

BACKGROUND

The present disclosure relates generally to the field of feedbackcontrollers. The present disclosure relates more specifically to systemsand methods for determining an appropriate sampling rate for a feedbackcontroller.

Feedback controllers are used to control a wide variety of systems andprocesses. Typically, a feedback controller receives a measured value ofa controlled variable (e.g., a feedback signal) and adjusts an inputprovided to a control device based on the measured value. The object offeedback controllers is to adjust the input provided to the device in away that maintains a controlled variable at a desired setpoint.

Many feedback controllers respond to a feedback signal based on one ormore control parameters. One control parameter frequently used infeedback control processes is a proportional gain (i.e., theproportional term, the gain, etc.). Feedback controllers typically applythe proportional gain as a multiplier to an error signal (e.g., adifference between a setpoint and a feedback signal) in determining aninput to provide to the controlled system or process. In addition to theproportional gain, feedback controllers can use other control parameterssuch as an integral term (e.g., in a proportional-integral (PI)controller) and/or a derivative term (e.g., in aproportional-integral-derivative (PID) controller, etc.).

For dynamic systems in which conditions outside of the control loopaffect the controlled variable or where an aspect of the control loop isvariably imperfect, the optimal control parameters may also be dynamic.Accordingly, some feedback controllers automatically adjust the controlparameters (e.g., the controller is “tuned”) based on observed behaviorof the system. Some feedback controllers include adaptive tuningalgorithms that automatically adjust the control parameters duringnormal operation. Such adaptive tuning algorithms can provide forimproved performance relative to other tuning strategies.

The rate at which measurements are collected from the controlled systemor process (e.g., the sampling rate) can affect the operation of anadaptive tuning algorithm. If the sampling rate is too fast, thefeedback controller may tune improperly and the proportional gain may betoo small. If the sampling rate is too slow, the performance of thefeedback controller may suffer. It is often challenging to determine anappropriate sampling rate for a feedback control system.

SUMMARY

One implementation of the present disclosure relates to a method foradaptively and automatically adjusting a sampling rate in a feedbackcontrol system. The method includes monitoring an error signal for adisturbance event, evaluating the error signal in response to thedisturbance event to estimate a time constant of a control process, anddetermining a sampling rate for use in the feedback control system basedon the estimated time constant. The error signal may be based on adifference between a setpoint and a feedback signal and the feedbacksignal may be received from the control process.

In some embodiments, monitoring the error signal for the disturbanceevent includes identifying the disturbance event as at least one of asetpoint change and a load disturbance. If the disturbance event isidentified as a setpoint change, evaluating the error signal in responseto the disturbance event may include tracking an area bounded by theerror signal in response to the setpoint change and dividing the trackedarea by a magnitude of the setpoint change to determine the estimatedtime constant of the control process. If the disturbance event isidentified as a load disturbance, evaluating the error signal inresponse to the disturbance event may include tracking a magnitude ofthe error signal in response to the load disturbance, determining a timeat which the magnitude of the error signal reaches a maximum in responseto the load disturbance, and subtracting a time at which the magnitudeof the error signal begins to increase in response to the loaddisturbance from the time at which the magnitude of the error signalreaches the maximum to determine the estimated time constant of thecontrol process.

In some embodiments, determining a sampling rate for use in the feedbackcontrol system includes selecting a sampling interval which is afraction of the estimated time constant. In more specific embodiments,determining a sampling rate for use in the feedback control systemincludes selecting a sampling interval between one-fortieth of theestimated time constant and the estimated time constant.

In some embodiments, the method further includes comparing thedetermined sampling rate with a previous sampling rate used by thefeedback control system and updating the previous sampling rate to thedetermined sampling rate if the comparison reveals that one or moreupdating criteria are met. The updating criteria may include updatingthe previous sampling rate to the determined sampling rate if thedetermined sampling rate is at least twice the previous sampling rate orno greater than half the previous sampling rate.

Another implementation of the present disclosure is a method forestimating a time constant of a process under closed loop feedbackcontrol. The method includes monitoring an error signal for adisturbance event, determining whether the disturbance event qualifiesas a setpoint change or a load disturbance, and evaluating the errorsignal in response to the determination of a setpoint change or a loaddisturbance to estimate a time constant of a control process. The errorsignal may be based on a difference between a setpoint and a feedbacksignal and the feedback signal may be received from the control process.

Evaluating the error signal in response to a setpoint change may includetracking an area bounded by the error signal in response to the setpointchange and dividing the tracked area by a magnitude of the setpointchange to determine the estimated time constant of the control process.Evaluating the error signal in response to a load disturbance mayinclude tracking a magnitude of the error signal in response to the loaddisturbance, determining a time at which the magnitude of the errorsignal reaches a maximum in response to the load disturbance, andsubtracting a time at which the magnitude of the error signal begins toincrease in response to the load disturbance from the time at which themagnitude of the error signal reaches the maximum to determine theestimated time constant of the control process.

Another implementation of the present disclosure is a feedback controlsystem for operating a control process. The feedback control systemincludes a process controller having a processing circuit configured tomonitor an error signal for a disturbance event, evaluate the errorsignal in response to the disturbance event to estimate a time constantof a control process, and determine a sampling rate for use in thefeedback control system based on the estimated time constant. The errorsignal may be based on a difference between a setpoint and a feedbacksignal and the feedback signal may be received from the control process.

In some embodiments, monitoring the error signal for the disturbanceevent includes identifying the disturbance event as at least one of asetpoint change and a load disturbance. If the disturbance event isidentified as a setpoint change, evaluating the error signal in responseto the disturbance event may include tracking an area bounded by theerror signal in response to the setpoint change and dividing the trackedarea by a magnitude of the setpoint change to determine the estimatedtime constant of the control process. If the disturbance event isidentified as a load disturbance, evaluating the error signal inresponse to the disturbance event may include tracking a magnitude ofthe error signal in response to the load disturbance, determining a timeat which the magnitude of the error signal reaches a maximum in responseto the load disturbance, and subtracting a time at which the magnitudeof the error signal begins to increase in response to the loaddisturbance from the time at which the magnitude of the error signalreaches the maximum to determine the estimated time constant of thecontrol process.

In some embodiments, determining a sampling rate for use in the feedbackcontrol system includes selecting a sampling interval no greater thanthe estimated time constant. In more specific embodiments, determining asampling rate for use in the feedback control system includes selectinga sampling interval approximately one-tenth of the estimated timeconstant.

In some embodiments, the processing circuit is further configured tocompare the determined sampling rate with a previous sampling rate usedby the feedback control system and update the previous sampling rate tothe determined sampling rate if the comparison reveals that one or moreupdating criteria are met. The updating criteria may include updatingthe previous sampling rate to the determined sampling rate if thedetermined sampling rate is at least twice the previous sampling rate orno greater than half the previous sampling rate.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a closed-loop control system including aproportional integral (PI) controller and a plant, illustrating theapplication of a setpoint r and a load disturbance d to the closed-loopsystem, according to an exemplary embodiment.

FIG. 2 is a block diagram of an adaptive feedback control systemincluding an adaptive feedback controller, a time constant estimatorconfigured to estimate a time constant τ_(p) for the plant based on anerror signal e, and a sampling rate adjustor configured to determine asampling rate h for the adaptive feedback controller based on theestimated time constant τ_(p), according to an exemplary embodiment.

FIG. 3 is a graph of the error signal e used by the adaptive feedbackcontrol system of FIG. 2 in response to a step change in the setpoint r,according to an exemplary embodiment.

FIG. 4 is a graph of the error signal e used by the adaptive feedbackcontrol system of FIG. 2 in response to a step change in the loaddisturbance d, according to an exemplary embodiment.

FIG. 5A is a graph of a feedback signal obtained from a controlledprocess as a function of time for several closed-loop control systems,illustrating the expected performance advantages of the adaptivefeedback control system of FIG. 2, according to an exemplary embodiment.

FIG. 5B is a graph of the sampling rate as a function of time as may bedetermined and used by the sampling rate adjustor of FIG. 2, accordingto an exemplary embodiment.

FIG. 5C is a graph of the controller gain parameter over time as may bedetermined and used by the adaptive feedback controller of FIG. 2 havingan adaptively updated sampling rate, as well as the controller gainparameter determined by an adaptive feedback controller with a fixedsampling rate, illustrating the expected performance advantage ofadaptively updating the sampling rate, according to an exemplaryembodiment.

FIG. 5D is a graph of the integral time parameter over time as may bedetermined and used by the adaptive feedback controller of FIG. 2 havingan adaptively updated sampling rate, as well as the integral timeparameter determined by an adaptive feedback controller with a fixedsampling rate, illustrating a performance advantage of adaptivelyupdating the sampling rate, according to an exemplary embodiment.

FIG. 6 is a detailed block diagram of the process controller of FIG. 2,according to an exemplary embodiment.

FIG. 7 is a flowchart of a process for adaptively adjusting a samplingrate in a feedback control system, according to an exemplary embodiment.

DETAILED DESCRIPTION

Before turning to the figures, which illustrate the exemplaryembodiments in detail, it should be understood that the disclosure isnot limited to the details or methodology set forth in the descriptionor illustrated in the figures. It should also be understood that theterminology is for the purpose of description only and should not beregarded as limited.

Referring generally to the figures, systems and methods for adaptivelyadjusting a sampling rate in a feedback control system are shown,according to various exemplary embodiments. The systems and methodsdescribed herein automatically estimate a time constant for a controlledprocess or system and automatically set the sampling rate based on theestimated time constant. The time constant is estimated by analyzing anerror signal (e.g., a difference between a setpoint and a feedbacksignal received from the controlled system).

Estimating the time constant includes determining whether the system issubject to a setpoint change or a load disturbance. If the system issubject to a setpoint change, the time constant is estimated byintegrating the error signal (e.g., numerically, analytically, etc.) todetermine an area under the error curve. The area under the error curvemay be divided by the magnitude of the setpoint change to determine theestimated time constant. If the system is subject to a load disturbance,the time constant may be estimated by determining a time at which theerror signal reaches an extremum (e.g., a minimum or a maximum) inresponse to the load disturbance. The time value at which the loaddisturbance begins may be subtracted from the time value at which theerror signal reaches the extremum to determine the estimated timeconstant. The estimated time constant may be used to automatically andadaptively set the sampling rate for the feedback control system,without manual observation or adjustment.

The systems and methods described herein may be incorporated into anexisting feedback controller (e.g., a proportional-integral (PI)controller, a proportional-integral-derivative (PID) controller, apattern recognition adaptive controller (PRAC), etc.) or supplement anexisting feedback control system. Advantageously, the adaptivelydetermined sampling rate may improve the adaptive feedback controller'sperformance in determining optimal control parameters (e.g., aproportional gain, an integral time, etc.) for the controlled process orsystem.

Referring now to FIG. 1, a block diagram of a closed-loop control system100 is shown, according to an exemplary embodiment. System 100 may be abuilding management system or part of a building management system(e.g., a HVAC control system, a lighting control system, a power controlsystem, a security system, etc.). System 100 may be a local ordistributed control system used to control a single building, a systemof buildings, one or more zones within a building. In someimplementations, system 100 may be a METASYS® brand control system assold by Johnson Controls, Inc. System 100 is shown to include a PIcontroller 102, a plant 104, a subtractor element 106, and a summationelement 108.

Plant 104 may be a system or process monitored and controlled byclosed-loop system 100 (e.g., a control process). Plant 104 may be adynamic system (e.g., a building, a system of buildings, a zone within abuilding, etc.) including one or more variable input devices (e.g.,dampers, air handling units, chillers, boilers, actuators, motors, etc.)and one or more measurement devices (e.g., temperature sensors, pressuresensors, voltage sensors, flow rate sensors, humidity sensors, etc.). Insome implementations, plant 104 may be a zone within a building (e.g., aroom, a floor, an area, etc.) and control system 100 may be used tocontrol temperature within the zone. For example, control system 100 mayactively adjust a damper position in a HVAC unit (e.g., an air handlingunit (AHU), a variable air volume (VAV) box, etc.) for increasing ordecreasing the flow of conditioned air (e.g., heated, chilled,humidified, etc.) into the building zone.

Plant 104 may receive an input from summation element 108 which combinesa control signal u with a disturbance signal d. In some embodiments,plant 104 may be modeled as a first-order plant having a transferfunction

${{G_{p}(s)} = {\frac{K_{p}}{1 + {\tau_{p}s}}e^{- {Ls}}}},$where τ_(p) is the dominant time constant, L is the time delay, andK_(p) is the process gain. In other embodiments, plant 104 may bemodeled as a second-order, third-order, or higher order plant. Plant 104may produce a feedback signal y in response to control signal u anddisturbance signal d. Feedback signal y may be subtracted from setpointr at subtractor element 106 to produce an error signal e (e.g., e=r−y).

PI controller 102 is shown receiving error signal e from subtractorelement 106. PI controller 102 may produce a control signal u inresponse to the error signal e. In some embodiments, controller 102 is aproportional-integral controller. PI controller 102 may have a transferfunction

${{G_{c}(s)} = \frac{K_{c}\left( {1 + {T_{i}s}} \right)}{T_{i}s}},$where K_(c) is the controller gain and T_(i) is the integral time.Controller gain K_(c) and integral time T_(i) are the control parameterswhich define the response of PI controller 102 to error signal e. Thatis, controller gain K_(c) and integral time T_(i) control how PIcontroller 102 translates error signal e into control signal u. In someembodiments, K_(c) and T_(i) are the only control parameters. In otherembodiments, different control parameters (e.g., a derivative controlparameter, etc.) may be used in addition to or in place of controlparameters K_(c) and T_(i).

Still referring to FIG. 1, in the Laplace domain, the error signal e(s)may be expressed in terms of the setpoint r(s) as

${e(s)} = {{r(s)}{\frac{1}{1 + {{G_{c}(s)}{G_{p}(s)}}}.}}$Error signal e(s) may be expressed in terms of the disturbance signald(s) as

${e(s)} = {{- {d(s)}}{G_{p}(s)}{\frac{1}{1 + {{G_{c}(s)}{G_{p}(s)}}}.}}$The common term in both expressions for the error signal may berewritten as

$\frac{1}{1 + {{G_{c}(s)}{G_{p}(s)}}} = {\frac{1}{1 + {\frac{\left( {K_{p}K_{c}} \right)\left( {1 + {T_{i}s}} \right)}{T_{i\;}{s\left( {1 + {\tau_{p}s}} \right)}}e^{- {Ls}}}}.}$

This expression can be simplified by assuming that K_(p) K_(c)≈1 andthat T_(i)≈τ_(p). The simplified closed-loop transfer function may thenbe expressed as

$\frac{1}{1 + {{G_{c}(s)}{G_{p}(s)}}} = {\frac{\tau_{p}s}{{\tau_{p}s} + e^{- {Ls}}}.}$

Referring now to FIG. 2, a block diagram of a closed-loop system 200 isshown, according to an exemplary embodiment. System 200 is shown toinclude a process controller 201 having an adaptive feedback controller210, a time constant estimator 214, and a sampling rate adjustor 216.Adaptive feedback controller 210 may be a pattern recognition adaptivecontroller (PRAC), a model recognition adaptive controller (MRAC), orany other type of adaptive tuning or feedback controller. PRACcontrollers are described in greater detail in U.S. Pat. Nos. 5,355,305,5,506,768, and 6,937,909, as well as other resources.

Adaptive feedback controller 210 may include a proportional-integral(PI) controller, a proportional-derivative (PD) controller, aproportional-integral-derivative (PID) controller, or any other type ofcontroller which generates a control signal in response to a feedbacksignal, an error signal, and/or a setpoint. Adaptive feedback controller210 may be any type of feedback controller (e.g., PRAC, MRAC, PI, etc.)which adaptively adjusts one or more controller parameters (e.g., aproportional gain, an integral time, etc.) used to generate the controlsignal. Adaptive feedback controller 210 is shown to include a PIcontroller 202 and an adaptive tuner 212.

PI controller 202 may be the same or similar to PI controller 102described in reference to FIG. 1. For example, PI controller 202 may bea proportional-integral controller having a transfer function

${G_{c}(s)} = {\frac{K_{c}\left( {1 + {T_{i}s}} \right)}{T_{i}s}.}$PI controller 202 may receive an error signal e from subtractor element206 and provide a control signal u to summation element 208. Summationelement 208 may combine control signal u with a disturbance signal d andprovide the combined signal to plant 204. Elements 206, 208, and plant204 may be the same or similar to elements 106, 108, and plant 104 asdescribed in reference to FIG. 1.

Adaptive tuner 212 may periodically adjust (e.g., calibrate, tune,update, etc.) the control parameters used by PI controller 202 intranslating error signal e into control signal u. The control parametersdetermined by adaptive tuner 212 may include a controller gain K_(c) andan integral time T_(i). Adaptive tuner 212 may receive control signal ufrom PI controller 202 and adaptively determine control parameters K_(c)and T_(i) based on control signal u (e.g., as described in theaforementioned U.S. patents). Adaptive tuner 212 provides the controlparameters K_(c) and T_(i) to PI controller 202.

Still referring to FIG. 2, system 200 is further shown to include a timeconstant estimator 214. Time constant estimator 214 determines adominant time constant τ_(p) for plant 204. The estimated time constantτ_(p) is then used by sampling rate adjuster 216 to adaptively determinean appropriate sampling rate h for PI controller 202. Time constantτ_(p) may also be used to predict the response of plant 204 to a givencontrol signal u. Time constant estimator 214 is shown receivingsetpoint r as well as error signal e. In other embodiments, timeconstant estimator 214 may receive only error signal e or may calculateerror signal e based on setpoint r and feedback signal y (e.g., e=r−y).Time constant estimator 214 may determine the dominant time constantτ_(p) based on error signal e, setpoint r, and/or other inputs receivedfrom various components of control system 200. In some embodiments, timeconstant estimator 214 may estimate a time constant based on controlsignal u (e.g., in a feed forward, model predictive control, and/or openloop control system). In some embodiments, control signal u may be usedin place of or in addition to error signal e in estimating a timeconstant.

The process used to estimate time constant τ_(p) may depend on whethersystem 200 is subject to a setpoint change or a load disturbance. Asetpoint change is an increase or decrease in setpoint r. A setpointchange may be instantaneous (e.g., a sudden change from a first setpointvalue to a second setpoint value) or gradual (e.g., a ramp increase ordecrease, etc.). A setpoint change may be initiated by a user (e.g.,adjusting a temperature setting on a thermostat) or received fromanother controller or process (e.g., a supervisory controller, an outerloop cascaded controller, etc.).

If system 200 is subject to a setpoint change, time constant estimator214 may estimate time constant τ_(p) by integrating the error signal e(e.g., numerically, analytically, etc.) to determine an area A under theerror curve. Time constant estimator 214 may then divide the area underthe error curve A by a magnitude of the setpoint change α to determinethe estimated time constant

${\tau_{p}\left( {{e.g.},{\tau_{p} = \frac{A}{a}}} \right)}.$

A load disturbance is an uncontrolled input applied to plant 204. Forexample, in a temperature control system for a building, the loaddisturbance may include heat transferred through the external walls ofthe building or through an open door (e.g., during a particularly hot orcold day). The load disturbance may be measured or unmeasured. In someembodiments, time constant estimator 214 receives a signal (e.g., astatus indicator, a process output, etc.) from adaptive feedbackcontroller 210 indicating whether system 200 is subject to a setpointchange or a load disturbance. In other embodiments, time constantestimator 214 determines whether a setpoint change or load disturbancehas occurred by analyzing the error signal e and/or setpoint r.

If system 200 is subject to a load disturbance, time constant estimator214 may estimate the time constant τ_(p) by determining a time t_(ex) atwhich the error signal e reaches an extremum (e.g., a minimum or amaximum) in response to the load disturbance. Time constant estimator214 may subtract a time at which the load disturbance begins t_(d) fromthe time at which error signal e reaches an extremum t_(ex) in responseto the load disturbance to determine the estimated time constant τ_(p)(e.g., r_(p)=t_(ex)−t_(d)). The systems and methods used to estimate thetime constant τ_(p) in response to a setpoint change and loaddisturbance are described in greater detail in reference to FIG. 3 andFIG. 4 respectively.

In some embodiments, time constant estimator 214 determines timeconstant τ_(p) in response to an identified load disturbance or setpointchange. Advantageously, time constant estimator 214 may determine timeconstant τ_(p) in real time (e.g., immediately after sufficient data hasbeen collected to perform the aforementioned calculations). For example,time constant estimator 214 may monitor error signal e for a sign change(e.g., positive to negative, negative to positive, zero crossings,etc.). Upon the occurrence of a load disturbance or setpoint change, theerror signal e may experience a “zero crossing” and increase or decreaseuntil reaching an extremum. PI controller 202 may attempt to reduce themagnitude of error signal e by manipulating control input u. Uponreaching a steady-state, error signal e may experience another “zerocrossing” as the error signal e approaches and/or crosses zero. Timeconstant estimator 214 may use the zero crossings as time boundaries forcalculating the area under error signal e or for calculating a timedifference between t_(d) and t_(ex).

In other embodiments, time constant estimator may determine τ_(p) usinghistorical disturbance data. In some embodiments, time constantestimator 214 is local to the controlled process or system for which thetime constant τ_(p) is estimated. In other embodiments, time constantestimator may be implemented remotely (e.g., in the “cloud,” on asupervisory level, etc.). Time constant estimator 214 may be part of PIcontroller 202, adaptive tuner 212, or implemented separately from suchcomponents.

In some embodiments, time constant estimator 214 determines whether adisturbance (e.g., a load disturbance or setpoint change) exceeds asignificance threshold before proceeding with the time constantestimation process. For example, time constant estimator 214 may comparea magnitude of the error signal e in response to the disturbance with athreshold value. The magnitude of the error signal e may be a maximum orminimum magnitude after the occurrence of a disturbance. In someembodiments, the threshold value is a noise threshold (e.g., an uppernoise threshold, a lower noise threshold, a noise band, etc.). Thethreshold value may be pre-defined (e.g., retrieved from memory,specified by a user, etc.) or automatically determined based onsteady-state measurements obtained from the controlled system orprocess. In other embodiments, the threshold value is an area threshold(e.g., an area under the error curve), a time threshold, or acombination thereof. For example, time constant estimator 214 maycompare the area under the error curve in response to a disturbance witha threshold area value. If the integrated area exceeds the thresholdvalue, time constant estimator 214 may determine that the disturbance issignificant. Time constant estimator 214 may proceed with the timeconstant estimation process if a disturbance is determined to besignificant. In some embodiments, time constant estimator 214 does notproceed to estimate the time constant τ_(p) if a disturbance is notdetermined to be significant. In other embodiments, time constantestimator 214 does not determine the significance of disturbances and/orestimates τ_(p) regardless of a determined significance.

Still referring to FIG. 2, system 200 is further shown to include asampling rate adjustor 216. Sampling rate adjustor 216 may receive theestimated time constant τ_(p) from time constant estimator 214 andcalculate a sampling rate h based on the estimated time constant τ_(p).In some embodiments, sampling rate h defines a sampling interval orsampling frequency used by PI controller 202 to obtain feedbackmeasurements from the controlled system or process (e.g., plant 204). Inother embodiments, sampling rate h defines a rate at which the controlsignal u is adjusted by PI controller 202. In further embodiments,sampling rate h defines a rate at which control parameters K_(c) andT_(i) are updated by adaptive tuner 212.

In some embodiments, sampling rate adjustor 216 may set sampling rate hto a value between one-fiftieth of the estimated time constant τ_(p) andthe estimated time constant

${\tau_{p}\left( {{e.g.},{\frac{\tau_{p}}{50} \leq h \leq \tau_{p}}} \right)}.$In more specific embodiments, the sampling rate h may be set to a valuebetween one-fortieth of the estimated time constant τ_(p) and theestimated time constant

${\tau_{p}\left( {{e.g.},{\frac{\tau_{p}}{40} \leq h \leq \tau_{p}}} \right)}.$In some embodiments, the sampling rate h may be set to a value betweenone-twentieth of the estimated time constant τ_(p) and one-third of theestimated time constant

${\tau_{p}\left( {{e.g.},{\frac{\tau_{p}}{20} \leq h \leq \frac{\tau_{p}}{3}}} \right)}.$In an exemplary embodiment, the sampling rate h may be set to a valueapproximately equal to one-tenth of the estimated time constant

${\tau_{p}\left( {{e.g.},{h \approx \frac{\tau_{p}}{10}}} \right)}.$In some embodiments, sampling rate adjustor 216 may be combined withtime constant estimator 214, PI controller 202, or adaptive tuner 212.

In some embodiments, sampling rate adjustor 216 compares the calculatedsampling rate h with a current or previous sampling rate h₀. If thecalculated sampling rate h differs significantly from h₀, the samplingrate may be updated to the recently calculated value h. In someembodiments, the current sampling rate h₀ is updated to the new samplingrate h if the new sampling rate h is greater than or equal to twice thecurrent sampling rate (e.g., h≥2h₀). In other embodiments, the currentsampling rate h₀ is updated to the new sampling rate h if the newsampling rate h is less than half the current sampling rate (e.g.,h≤0.5h₀). In further embodiments, sampling rate adjustor 216 may updatethe current sampling rate h₀ if the difference between the currentsampling rate h₀ and the calculated sampling rate h exceeds a differencethreshold (e.g., |h₀−h|>threshold) or if the ratio between h₀ and hexceeds a ratio threshold

$\left( {{e.g.},{\frac{h_{0}}{h} > {threshold}}} \right).$The updated sampling rate h may be communicated to adaptive feedbackcontroller 210.

Advantageously, a properly set sampling rate h (e.g., a sampling ratewhich is a function of the process time constant τ_(p)), may provideimproved stability and control functionality for adaptive feedbackcontroller 210. Adaptively and automatically determining sampling rate hmay eliminate the need for human intervention (e.g., a trial and errorapproach or a rough estimation of the proper sampling rate) to properlyconfigure a wide variety of control systems.

Referring now to FIG. 3, a graph 300 illustrating the time response oferror signal e to a change in setpoint r is shown, according to anexemplary embodiment. Graph 300 shows error signal e as a function oftime in response to an step increase of magnitude α in setpoint r. Insome embodiments, the output y of plant 204 is a continuous variableunable to instantaneously increase or decrease. Because the error signale is defined as the difference between setpoint r and output y (e.g.,e=r−y), the error signal e may suddenly increase from a first value(e.g., e=0) immediately before the setpoint change to a second valueimmediately after the setpoint change. The second value may equal themagnitude α of the setpoint change. PI controller 202 may respond to theincrease in error signal e by adjusting the control signal u applied toplant 204. Such adjustment may cause error signal e to continuouslydecrease from the magnitude α of the setpoint change to a steady statevalue (e.g., e=0).

Still referring to FIG. 3, time constant estimator 214 may estimate thetime constant τ_(p) for plant 204 based on the response of error signale to a step change in setpoint r. As was previously mentioned, in theLaplace domain the error signal e(s) may be expressed in terms of thesetpoint r(s) as

${{e(s)} = {{r(s)}\frac{1}{1 + {{G_{c}(s)}{G_{p}(s)}}}}},{where}$$\frac{1}{1 + {{G_{c}(s)}{G_{p}(s)}}} = {\frac{\tau_{p}s}{{\tau_{p}s} + e^{- {Ls}}}.}$A step change of magnitude α in the setpoint produces the error signal

${e(s)} = {\frac{a\;\tau_{p}}{{\tau_{p}s} + e^{- {Ls}}}.}$The area under the error curve in graph 300 may be determined byintegrating the error signal e(s) (e.g.,

${e(s)}{\left( {{e.g.},{{I(s)} = {\frac{1}{s}{e(s)}}}} \right).}$In a stable system, the area A under the curve can be expressed as thedifference in the areas at t=∞ and t=0. That is,

$A = {{{\lim\limits_{s\rightarrow 0}\left\{ {{sI}(s)} \right\}} - {\lim\limits_{s\rightarrow\infty}\left\{ {{sI}(s)} \right\}}} = {a\;{\tau_{p}.}}}$From this expression, it is apparent that the time constant τ_(p),depends only on the magnitude α of the setpoint change and the area Aunder the error curve.

Time constant estimator 214 may track the area A under the error curvein response to a setpoint change and estimate the time constant τ_(p) ,according to the equation

$\tau_{p} = {\frac{A}{a}.}$The area A under the error curve may be tracked by multiplying themagnitude of the error signal e at each time step k by the duration ofan interval between time steps

$\left( {{e.g.},{A = {\sum\limits_{k = 1}^{n}\;{{{e_{k}(t)} \cdot \Delta}\; t_{k}}}}} \right).$In some embodiments, the magnitude α of the setpoint change may beestimated based on the magnitude of the error signal e immediately afterthe setpoint change. In other embodiments, the magnitude α of thesetpoint change may be determined by analyzing setpoint r or may bereceived as an input from adaptive feedback controller 210.

Still referring to FIG. 3, in some embodiments, time constant estimator214 determines a time delay L for the controlled system or process (e.g.plant 204). The time delay L may represent an interval between the timeat which an input is applied to a controlled system and the time atwhich the input begins to take effect. Time constant estimator 214 maydetermine time delay L by analyzing the response of error signal e to asetpoint change. For example, graph 300 shows the error signal einstantaneously changing to the magnitude α of the setpoint changeimmediately after the setpoint change occurs. The error signal e maymaintain this value until after time delay L has passed and the dynamicsof the system begin to take effect. Time constant estimator 214 mayestimate the time delay L by subtracting a time at which the setpointchange occurs from the time at which the magnitude of the error signal ebegins to decrease (e.g., in response to an adjusted control input u).In some embodiments, time constant τ_(p), and time delay L may beseparately determined. In other embodiments, time constant τ_(p) andtime delay L may be combined into a single variable (e.g., an averageresidence time, a dominant time constant, etc.)

Referring now to FIG. 4, a graph 400 illustrating the time response oferror signal e to a load disturbance is shown, according to an exemplaryembodiment. The load disturbance may be applied to plant 204 as anuncontrolled and/or unmeasured input. The load disturbance may cause achange in the output y received from plant 204 and consequently in errorsignal e (e.g., e=r−y). In some embodiments, the output y of plant 204is a continuous variable unable to instantaneously increase or decrease.If the setpoint r is held constant, a load disturbance may cause acontinuous increase or decrease in the error signal e (e.g., rather thanthe instantaneous increase or decrease caused by a setpoint change).Graph 400 shows the error signal e continuously decreasing in responseto a load disturbance. The error signal e is shown decreasing from aninitial value (e.g. e=0) to a minimum value e_(min). In otherembodiments, the load disturbance may cause an increase in the errorsignal from an initial value (e.g., e=0) to a maximum value e_(max).

In the Laplace domain, the response of the error signal e to a stepchange of magnitude α a in the load disturbance may be represented bythe equation

${{e(s)} = {\frac{{aK}_{p}\tau_{p}}{\left( {{\tau_{p}s} + 1} \right)\left( {{\tau_{p}s} + e^{- {Ls}}} \right)}e^{- {Ls}}}},$where K_(p) is the process gain and L is the time delay of thecontrolled system or process (e.g., plant 204). When a load disturbanceoccurs, the dynamics of the system do not begin to affect the errorsignal e until after the time delay L. Accordingly, the time delay L maybe neglected and the response of the error signal e to a step change ofmagnitude α in the load disturbance may be represented by the equation

${e(s)} = {\frac{{aK}_{p}\tau_{p}}{\left( {{\tau_{p}s} + 1} \right)^{2}}.}$

In the time domain, the error signal e may be expressed as

${e(t)} = {{aK}_{p}\tau_{p}{{te}^{\frac{- t}{\tau_{p}}}.}}$The derivative of this expression is

${\overset{.}{e}(t)} = {{aK}_{p}\tau_{p}{{{te}^{\frac{- t}{\tau_{p}}}\left\lbrack {1 - \frac{t}{\tau_{p}}} \right\rbrack}.}}$An extremum (e.g., a maximum or minimum) of the error signal is found attime t_(ex) when ė(t)=0. The extremum of the error signal e in responseto a load disturbance may occur at a time approximately equal to thetime constant τ_(p) after the disturbance has taken effect. Timeconstant estimator 214 may determine time constant τ_(p) by subtractinga time at which the magnitude of error signal e begins to increase t_(d)in response to a load disturbance from a time at which error signal ereaches an extremum t_(ex) in response to the load disturbance (e.g.,τ_(p)=t_(ex)−t_(d)).

Referring now to FIGS. 5A-5D, a series of graphs illustrating theexpected advantages of adaptively updating sampling rate h are shown,according to an exemplary embodiment. In FIGS. 5A-5D, a simulated firstorder plant is provided with a control signal u determined by threedifferent types of controllers—a proportional integral (PI) controllerhaving optimal controller parameters (PI_(opt)), a pattern recognitionadaptive controller (PRAC) having a fixed sampling rate h(PRAC_(fixed)), and a PRAC with an adaptively adjusted sampling rate h(e.g., using the systems and methods described in reference to FIGS.2-4) (PRAC_(adaptive)).

Referring specifically to FIG. 5A, a graph 501 is shown illustrating theresultant measured variable y as a function of time when the simulatedplant is independently subjected to a series of setpoint changes andload disturbances. The setpoint r is shown by line 510 and theperformance of PI_(opt), PRAC_(fixed), and PRAC_(adaptive) are shown bylines 520, 530, and 540 respectively. As can be seen from FIG. 5A,PRAC_(adaptive) (line 540) demonstrates a superior ability to tracksetpoint r (e.g., control the measured variable y to equal the setpoint)when compared with PRAC_(fixed) (line 530). The performance ofPRAC_(adaptive) may even exceed the performance of PI_(opt) (line 520).

Referring to FIG. 5B, a graph 502 is shown illustrating the samplingrate h as a function of time for PRAC_(adaptive). The sampling rate h isshown starting at a first value at t=0. At approximately t=250 seconds,the sampling rate h is adjusted to a lower value. Referring again toFIG. 5A, at approximately this same time (e.g., t≈250 seconds), theperformance of PRAC_(adaptive) significantly improves. Notably,PRAC_(adaptive) is shown to adjust the sampling rate h only oncethroughout the simulation. The single sampling rate adjustment maysuggest that time constant τ_(p) estimation (e.g., as described inreference to time constant estimator 214) and subsequent sampling rateadjustment (e.g., by sampling rate adjustor 216) accurately capture thetrue time constant τ_(p) of the simulated plant.

Referring to FIGS. 5C and 5D, graphs 503 and 504 are shown illustratingthe controller gain parameter K_(c) and integral time parameter T_(i)(e.g., determined by adaptive tuner 212) as a function of time forPRAC_(fixed) and for PRAC_(adaptive). In FIG. 5C, line 550 illustratesthe controller gain parameter K_(c) for PRAC_(fixed) and line 560illustrates the gain parameter K_(c) for PRAC_(adaptive). In FIG. 5D,line 570 illustrates the integral time parameter T_(i) for PRAC_(fixed)and line 580 illustrates the integral time parameter T_(i) forPRAC_(adaptive). At approximately t=250 seconds (i.e., the same timethat the sampling rate h is adjusted), PRAC_(adaptive) compensates byadjusting the controller gain K_(c) from an initial value to a lowervalue and by adjusting the integral time T_(i) from an initial value toa lower value. Notably, PRAC_(adaptive) is shown to adjust thecontroller gain K_(c) and integral time T_(i) only one time throughoutthe simulation. This single adjustment may suggest that once thesampling rate h is properly set, PRAC_(adaptive) can accuratelydetermine the appropriate controller gain K_(c) and integral time T_(i)without requiring subsequent correction.

Referring now to FIG. 6, a block diagram of process controller 201 isshown, according to an exemplary embodiment. Process controller 201 isshown to include a communications interface 610 and a processing circuit620. Communications interface 610 may include any number of jacks, wireterminals, wire ports, wireless antennas, or other communicationsadapters, hardware, or devices for communicating information (e.g.,setpoint r information, error signal e information, feedback signal yinformation, etc.) or control signals (e.g., a control signal u, etc.)Communications interface 610 may be configured to send or receiveinformation and/or control signals between process controller 201 and acontrolled system or process (e.g., plant 204), between processcontroller 201 and a supervisory controller, or between processcontroller 201 and a local controller (e.g., a device, building, ornetwork specific controller). Communications interface 610 may beconfigured to send or receive information over a local area network(LAN), wide area network (WAN), and/or a distributed network such as theInternet. Communications interface 610 can include communicationselectronics (e.g., receivers, transmitters, transceivers, modulators,demodulators, filters, communications processors, communication logicmodules, buffers, decoders, encoders, encryptors, amplifiers, etc.)configured to provide or facilitate the communication of the signalsdescribed herein.

Processing circuit 620 is shown to include a processor 630 and memory640. Processor 630 can be implemented as a general purpose processor, anapplication specific integrated circuit (ASIC), one or more fieldprogrammable gate arrays (FPGAs), a group of processing components, orother suitable electronic processing components.

Memory 640 (e.g., memory device, memory unit, storage device, etc.) isone or more devices (e.g., RAM, ROM, Flash memory, hard disk storage,etc.) for storing data and/or computer code for completing orfacilitating the various processes, layers and modules described in thepresent disclosure. Memory 640 may be or include volatile memory ornon-volatile memory. Memory 136 may include database components, objectcode components, script components, or any other type of informationstructure for supporting the various activities and informationstructures described in the present application. According to anexemplary embodiment, memory 640 is communicably connected to processor630 via processing circuit 620 and includes computer code for executing(e.g., by processing circuit 620 and/or processor 630) one or moreprocesses described herein. Memory 640 is shown to include a timeconstant estimation module 642, a sampling rate adjustment module 644,and an adaptive feedback control module 646.

Time constant estimation module 642 may be configured to perform thefunctions of time constant estimator 214 as described in reference toFIG. 2. Time constant estimation module 642 may receive an error signale, a setpoint signal r, and or a feedback signal y. Time constantestimation module 642 may be configured to monitor the error signal eand estimate a time constant τ_(p) for a controlled system or processbased on the error signal e. In some implementations, time constantestimation module 642 may determine whether the controlled system is toa setpoint change or a load disturbance (e.g., by receiving a signalfrom adaptive feedback control module 646, by analyzing the error signale, etc.).

If the system is subject to a setpoint change, time constant estimationmodule 642 may estimate the time constant τ_(p) by determining an areaunder the error curve (e.g., defined by error signal e). The area underthe error curve may be divided by the magnitude of the setpoint changeto determine the estimated time constant τ_(p). If the system is subjectto a load disturbance, the time constant τ_(p) may be estimated bydetermining a time at which the error signal e reaches an extremum(e.g., a minimum or a maximum) in response to the load disturbance. Timeconstant estimation module 642 may subtract the time value at which theload disturbance begins from the time value at which the error signal ereaches an extremum to determine the estimated time constant τ_(p). Theerror signal e may be monitored for zero crossings (e.g., a sign changefrom positive to negative or negative to positive) to determine the timeat which a load disturbance begins. Time constant estimation module 642may communicate the estimated time constant τ_(p) to sampling rateadjustment module 644.

Sampling rate adjustment module 644 may be configured to perform thefunctions of sampling rate adjustor 216 as described in reference toFIG. 2. Sampling rate adjustment module 644 may receive the estimatedtime constant τ_(p) from time constant estimation module 642 andcalculate a sampling rate h based on the estimated time constant τ_(p).In some embodiments, sampling rate adjustment module 644 may set thesampling rate h to a value approximately equal to one-tenth of theestimated time constant τ_(p) (e.g.,

${\tau_{p}\left( {{e.g.},{h \approx \frac{\tau_{p}}{10}}} \right)}.$In some embodiments, sampling rate adjustment module 644 compares thecalculated sampling rate h with a current or previous sampling rate h₀.If the calculated sampling rate h differs significantly from h₀ (e.g., his less than half h₀ or greater than twice h₀), sampling rate adjustmentmodule may update the sampling rate to the recently calculated value h.The updated sampling rate h may be communicated to adaptive feedbackcontrol module 646.

Adaptive feedback control module 646 may be configured to perform thefunctions of PI controller 202 and adaptive tuner 212 as described inreference to FIG. 2. Adaptive feedback control module 646 may includethe functionality of a pattern recognition adaptive controller (PRAC), amodel recognition adaptive controller (MRAC), or any other type ofadaptive tuning or feedback controller. Adaptive feedback control module646 may receive an error signal e representing a difference between afeedback signal y and a setpoint r. Adaptive feedback control module 646may calculate a control signal u for a controlled process or systembased on the error signal e. The control signal u may be communicated tothe controlled process or system via communications interface 610.

Referring now to FIG. 7, a flowchart of a process 700 for adaptivelyadjusting a sampling rate in a feedback control system is shown,according to an exemplary embodiment. Process 700 is shown to includemonitoring an error signal for a disturbance event (step 702). The errorsignal e may be a difference between a setpoint r and a feedback signaly received from a control process or system. In some embodiments, step702 includes determining whether a disturbance in the error signal e(e.g., a deviation in the error signal from a zero error steady state)qualifies as a disturbance event. Step 702 may involve comparing amagnitude of the error signal e or an area bounded by the error signal eto a threshold value. In some embodiments, the threshold value may be anoise threshold (e.g., measurement noise, process noise, combined noise,etc.). If the magnitude or area exceeds the threshold value, thedisturbance may be classified as a disturbance event. In someembodiments, the remaining steps of process 700 (e.g., steps 704-710)are only performed if a detected disturbance qualifies as a disturbanceevent. In other embodiments, steps 704-710 are performed for alldetected disturbances.

Step 702 may include identifying the disturbance event as at least oneof a setpoint change and a load disturbance. In some embodiments, thedisturbance event may be identified via a status indicator or signalreceived from an adaptive feedback controller. For example, a PRAC mayoutput a signal indicating whether the control system is subject to asetpoint change or a load disturbance. In other embodiments, thedisturbance event may be identified by analyzing the error signal e. Forexample, a setpoint change may result in an instantaneous change in theerror signal e whereas a load disturbance may result in continuousincrease in the magnitude of the error signal e.

Still referring to FIG. 7, process 700 is shown to further includeevaluating the error signal in response to the disturbance event toestimate a time constant for a control process (step 704). If thedisturbance event is identified as a setpoint change in step 702,evaluating the error signal e may involve tracking an area A bounded bythe error signal e in response to the setpoint change. The area Abounded by the error signal may be an area between an error curve (e.g.,a graphical representation of the error signal as a function of time)and the time axis (e.g., a “zero error” line extending along the timeaxis). The area A bounded by the error signal may be an area above thetime axis (e.g., if the error curve includes positive error values) oran area below the time axis (e.g., if the error curve includes negativeerror values). The area A bounded by the error signal may be trackedanalytically (e.g., by expressing the error signal as an equation,integrating the equation, A=∫₀ ^(x) e(t)dt, etc.) or numerically (e.g.,by multiplying a magnitude of the error signal by a duration of a timestep, adding the resultant products,

${A = {\sum\limits_{k = 1}^{n}\;{{{e_{k}(t)} \cdot \Delta}\; t_{k}}}},$etc.).

In some embodiments, the area A bounded by the error signal e may betracked during a tracking interval. The tracking interval may begin atthe time of the setpoint change and end at a time when the error signale crosses the time axis (e.g., a “zero crossing”). In other embodiments,the tracking interval may end at a time when a magnitude of the errorsignal |e| crosses a magnitude threshold. The magnitude threshold may bea non-zero error value at which it may be determined that the controlsystem has adequately responded to the disturbance event. In someembodiments, the magnitude threshold may be a noise threshold (e.g.,measurement noise, process noise, etc.) for the controlled system orprocess.

If the disturbance event is identified as a setpoint change in step 702,step 704 may further include dividing the area A bounded by the errorsignal by a magnitude α of the setpoint change to determine theestimated time constant of the control process

$\left( {{e.g.},{\tau_{p} = \frac{A}{a}}} \right).$In some embodiments, the magnitude of the setpoint change may beobtained by analyzing the setpoint signal (e.g., subtracting a setpointvalue before the setpoint change from a setpoint value after thesetpoint change). In other embodiments, the magnitude α of the setpointchange may be obtained by analyzing the error signal e (e.g.,determining the magnitude of the instantaneous increase in the magnitudeof the error signal). In further embodiments, the magnitude α of thesetpoint change may be received from another process or system.

Still referring to step 704, if the disturbance event is identified as aload disturbance in step 702, evaluating the error signal in response tothe disturbance event may include tracking a magnitude of the errorsignal |e| in response to the load disturbance and determining a time atwhich the magnitude of the error signal |e| reaches a maximum inresponse to the load disturbance. The maximum magnitude of the errorsignal |e|_(max) may be an extremum (e.g., a maximum value e_(max) orminimum value e_(min)) in response to the load disturbance. Unlikesetpoint changes, load disturbances may cause the magnitude of the errorsignal |e| to increase continuously (e.g., non-instantaneously) untilreaching a maximum |e|_(max) at a time t_(ex) after the disturbanceoccurs. If the disturbance event is identified as a load disturbance instep 702, step 704 may involve subtracting a time t_(d) at which themagnitude of the error signal begins to increase in response to the loaddisturbance from the time at which the magnitude of the error signalreaches the maximum t_(ex) to determine the time constant of the controlprocess (e.g., τ_(p)=t_(ex)−t_(d)).

Still referring to FIG. 7, process 700 is shown to further includedetermining a sampling rate for use in the feedback control system basedon the estimated time constant (step 706). The sampling rate h may be asampling period (e.g., an interval between samples) or a samplingfrequency (e.g., a rate at which samples are obtained). In someembodiments, the sampling rate h may be used to select a subset ofmeasurements from a feedback signal y for use in determining a controlsignal u to be applied to a controlled process. In other embodiments,the sampling rate h may specify the interval at which the control signalu is updated. In some embodiments, step 706 may involve selecting asampling rate h between one-fortieth of the estimated time constantτ_(p) and the estimated time constant

${\tau_{p}\left( {{e.g.},{\frac{\tau_{p}}{40} \leq h \leq \tau_{p}}} \right)}.$In a more specific embodiment, step 706 may involve selecting a samplingrate h approximately one-tenth of the estimated time constant

${\tau_{p}\left( {{e.g.},{h \approx \frac{\tau_{p}}{10}}} \right)}.$

Still referring to FIG. 7, in some embodiments, process 700 may furtherinclude comparing the determined sampling rate h with a previoussampling rate h₀ used by the feedback control system (step 708) andupdating the previous sampling rate h₀ to the determined sampling rate hif the comparison reveals that one or more updating criteria are met(step 710). The updating criteria may prevent the previous sampling rateh₀ from being updated if the change would be minimal or insignificant.For example, the updating criteria may include updating the previoussampling rate h₀ to the sampling rate h determined in step 706 if thedetermined sampling rate h is at least twice the previous sampling rate(e.g., h≥2h₀). In some embodiments, the previous sampling rate h₀ may beupdated to the sampling rate h determined in step 706 if the determinedsampling rate h is no greater than half the previous sampling rate(e.g., h≤0.5h₀). In further embodiments, steps 708 and 710 may involveupdating the previous sampling rate h₀ if the difference between theprevious sampling rate h₀ and the sampling rate h determined in step 706exceeds a difference threshold (e.g., |h₀−h|>threshold) or if the ratiobetween h₀ and h exceeds a ratio threshold

$\left( {{e.g.},{\frac{h_{0}}{h} > {threshold}},{\frac{h}{h_{0}} > {threshold}},{{etc}.}} \right).$

In some implementations, the systems and methods described herein may beused in a closed-loop feedback control system. When implemented in aclosed-loop system, a disturbance event may be detected by monitoring anerror signal (e.g., for a load disturbance or a setpoint change). Theerror signal may be based on a feedback signal received from a controlprocess. In other implementations, the described systems and methods maybe used in a feed-forward control system, and open loop control system,a model predictive control system, a cascaded control system, and/or anyother type of automated control system. When implemented in non-feedbackcontrol systems, the disturbance event may be detected by monitoring acontrol signal (e.g., provided to a control process), a feed-forwardsignal (e.g., received from a feed-forward estimator), a sensor signal(e.g., from a sensor monitoring a variable other than the controlledvariable), or any other type of signal (e.g., calculated or measured)communicated between one or more components of the control system. Themonitored signal may be analyzed as described above (e.g., by timeconstant estimator 214) for estimating a time constant and determining asampling rate for use in the non-feedback control system.

The construction and arrangement of the systems and methods as shown inthe various exemplary embodiments are illustrative only. Although only afew embodiments have been described in detail in this disclosure, manymodifications are possible (e.g., variations in sizes, dimensions,structures, shapes and proportions of the various elements, values ofparameters, mounting arrangements, use of materials, colors,orientations, etc.). For example, the position of elements may bereversed or otherwise varied and the nature or number of discreteelements or positions may be altered or varied. Accordingly, all suchmodifications are intended to be included within the scope of thepresent disclosure. The order or sequence of any process or method stepsmay be varied or re-sequenced according to alternative embodiments.Other substitutions, modifications, changes, and omissions may be madein the design, operating conditions and arrangement of the exemplaryembodiments without departing from the scope of the present disclosure.

The present disclosure contemplates methods, systems and programproducts on any machine-readable media for accomplishing variousoperations. The embodiments of the present disclosure may be implementedusing existing computer processors, or by a special purpose computerprocessor for an appropriate system, incorporated for this or anotherpurpose, or by a hardwired system. Embodiments within the scope of thepresent disclosure include program products comprising machine-readablemedia for carrying or having machine-executable instructions or datastructures stored thereon. Such machine-readable media can be anyavailable media that can be accessed by a general purpose or specialpurpose computer or other machine with a processor. By way of example,such machine-readable media can comprise RAM, ROM, EPROM, EEPROM, CD-ROMor other optical disk storage, magnetic disk storage or other magneticstorage devices, or any other medium which can be used to carry or storedesired program code in the form of machine-executable instructions ordata structures and which can be accessed by a general purpose orspecial purpose computer or other machine with a processor. Combinationsof the above are also included within the scope of machine-readablemedia. Machine-executable instructions include, for example,instructions and data which cause a general purpose computer, specialpurpose computer, or special purpose processing machines to perform acertain function or group of functions.

Although the figures show a specific order of method steps, the order ofthe steps may differ from what is depicted. Also two or more steps maybe performed concurrently or with partial concurrence. Such variationwill depend on the software and hardware systems chosen and on designerchoice. All such variations are within the scope of the disclosure.Likewise, software implementations could be accomplished with standardprogramming techniques with rule based logic and other logic toaccomplish the various connection steps, processing steps, comparisonsteps and decision steps.

What is claimed is:
 1. A control system for a plant, the control system comprising: a controller having a processing circuit configured to: detect a disturbance in the control system; classify the disturbance as a setpoint change or a load disturbance; in response to detecting the disturbance, evaluate a signal affected by the disturbance to estimate a response time of a plant, wherein the response time is a parameter that characterizes a response of the plant to the disturbance and, if the disturbance is classified as a setpoint change, the controller is configured to estimate the response time by: identifying a portion of the signal affected by the disturbance; tracking an area bounded by the identified portion of the signal; and dividing the area bounded by the identified portion of the signal by a magnitude of the setpoint change to determine the estimated response time; adjust an operating parameter used by the control system based on the estimated response time; and use the adjusted operating parameter to generate and provide an input to the plant.
 2. The control system of claim 1, wherein the controller is configured to identify the portion of the signal affected by the disturbance by: determining a start time at which the setpoint change occurs; determining an end time at which a magnitude of the signal crosses a magnitude threshold; and identifying a portion of the signal beginning at the start time and ending at the end time as the portion of the signal affected by the disturbance.
 3. The control system of claim 1, wherein the controller is configured to track the area bounded by the identified portion of the signal by: determining a magnitude of the signal at a plurality of discrete time steps along the identified portion of the signal; determining an integrated signal value for each time step by multiplying the magnitude of the signal at each time step by a duration of an interval between the time steps; and summing the integrated signal values associated with each of the time steps along the identified portion of the signal.
 4. The control system of claim 1, wherein if the disturbance is classified as a load disturbance, the controller is configured to evaluate the signal affected by the disturbance by: identifying a portion of the signal affected by the disturbance; tracking a magnitude of the signal during the identified portion to determine a time at which the magnitude of the signal reaches an extremum in response to the load disturbance; subtracting a time at which the magnitude of the signal begins to change in response to the load disturbance from the time at which the magnitude of the signal reaches the extremum to determine the estimated response time.
 5. The control system of claim 1, wherein the controller is configured to evaluate the signal to estimate the response time by evaluating a portion of the signal that occurs during a deviation from steady-state operation of the control system.
 6. The control system of claim 1, wherein: the operating parameter used by the control system is a sampling interval; and the controller is configured to adjust the operating parameter by selecting a sampling interval which is a fraction of the estimated response time.
 7. The control system of claim 1, wherein the response time comprises at least one of a dominant time constant, a bandwidth, and an open loop response time of the plant.
 8. The control system of claim 1, wherein the controller is configured to adjust the operating parameter used by the control system by: determining a new value of the operating parameter based on the estimated response time; comparing the new value of the operating parameter to a previous value of the operating parameter used by the control system; and updating the operating parameter to the new value if the new value is greater than twice the previous value or less than half the previous value.
 9. A method for adaptively and automatically adjusting an operating parameter in a control system, the method comprising: detecting a disturbance in the control system, wherein detecting the disturbance in the control system comprises classifying the disturbances as a setpoint change or a load disturbance; in response to detecting the disturbance, evaluating a signal affected by the disturbance to estimate a response time of a plant, wherein the response time is a parameter that characterizes a response of the plant to the disturbance and, if the disturbance is classified as a setpoint change, evaluating the signal affected by the disturbance comprises: identifying a portion of the signal affected by the disturbance; tracking an area bounded by the identified portion of the signal; and dividing the area bounded by the identified portion of the signal by a magnitude of the setpoint change to determine the estimated response time; adjusting an operating parameter used by the control system based on the estimated response time; and using the adjusted operating parameter to generate and provide an input to the plant.
 10. The method of claim 9, wherein identifying the portion of the signal affected by the disturbance comprises: determining a start time at which the setpoint change occurs; determining an end time at which a magnitude of the signal crosses a magnitude threshold; and identifying a portion of the signal beginning at the start time and ending at the end time as the portion of the signal affected by the disturbance.
 11. The method of claim 9, wherein tracking the area bounded by the identified portion of the signal comprises: determining a magnitude of the signal at a plurality of discrete time steps along the identified portion of the signal; determining an integrated signal value for each time step by multiplying the magnitude of the signal at each time step by a duration of an interval between the time steps; and summing the integrated signal values associated with each of the time steps along the identified portion of the signal.
 12. The method of claim 9, wherein if the disturbance is classified as a load disturbance, evaluating the signal affected by the disturbance comprises: identifying a portion of the signal affected by the disturbance; tracking a magnitude of the signal during the identified portion to determine a time at which the magnitude of the signal reaches an extremum in response to the load disturbance; subtracting a time at which the magnitude of the signal begins to change in response to the load disturbance from the time at which the magnitude of the signal reaches the extremum to determine the estimated response time.
 13. The method of claim 9, wherein evaluating the signal to estimate the response time comprises evaluating a portion of the signal that occurs during a deviation from steady-state operation of the control system.
 14. The method of claim 9, wherein: the operating parameter used by the control system is a sampling interval; and adjusting the operating parameter comprises selecting a sampling interval which is a fraction of the estimated response time.
 15. The method of claim 9, wherein the response time comprises at least one of a dominant time constant, a bandwidth, and an open loop response time of the plant.
 16. One or more non-transitory computer-readable media having instructions for adaptively and automatically adjusting an operating parameter in a control system stored therein, the instructions being executable by one or more processors to cause the one or more processors to perform operations comprising: detecting a disturbance in the control system, wherein detecting the disturbance in the control system comprises classifying the disturbances as a setpoint change or a load disturbance; in response to detecting the disturbance, evaluating a signal affected by the disturbance to estimate a response time of a plant, wherein the response time is a parameter that characterizes a response of the plant to the disturbance and, if the disturbance is classified as a setpoint change, evaluating the signal affected by the disturbance comprises: identifying a portion of the signal affected by the disturbance; tracking an area bounded by the identified portion of the signal; and dividing the area bounded by the identified portion of the signal by a magnitude of the setpoint change to determine the estimated response time; adjusting an operating parameter used by the control system based on the estimated response time; and using the adjusted operating parameter to generate and provide an input to the plant. 